I'm starting to work my way through Algebra I by Jacobson after being out of college for 15 years, and he's using an expression I don't remember from college algebra.
It's a number over a number without a line between. I assume it means "n divided by 1", is this correct?

The symbol ${n \choose k}$ is called a binomial coefficient, and it is read as "n choose k". It is the number of ways to choose $k$ objects, unordered, from a collection of $n$ objects. It is equal to $\frac{n!}{k!(n-k)!}$, where "!" denotes factorial.